COM of Continuous Bodies — JEE Main Physics MCQs with Solutions
Free JEE Main Physics COM of Continuous Bodies MCQs with step-by-step solutions (8 questions). Part of Centre of Mass, Momentum & Collisions. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — COM of Continuous Bodies · easy · theory
The centre of mass of a uniform semicircular RING of radius R lies on the symmetry axis at a distance from the centre of:
A. 4R/3π
B. 2R/π ✓ Correct
C. R/π
D. R/2
Solution: Standard results: semicircular ring 2R/π; semicircular DISC 4R/3π — don't swap them.
Q2 — COM of Continuous Bodies · medium · theory
The COM of a uniform solid HEMISPHERE of radius R lies above the flat face at:
A. R/2
B. 2R/π
C. 3R/5
D. 3R/8 ✓ Correct
Solution: Solid hemisphere: 3R/8. (Hollow hemispherical shell: R/2; solid cone: h/4 above the base.)
Q3 — COM of Continuous Bodies · easy · numerical
A uniform rod of length 2 m has its centre of mass at a distance from one end of:
A. 0.5 m
B. 2/3 m
C. 1 m ✓ Correct
D. 1.5 m
Solution: A uniform rod's COM is at its midpoint: L/2 = 1 m.
Q4 — COM of Continuous Bodies · medium · numerical
A rod of length 1 m has linear density λ = 2x (kg/m). The COM from the light end (x = 0) is at:
A. 2/3 m ✓ Correct
B. 1/2 m
C. 3/4 m
D. 1/3 m
Solution: x_cm = ∫xλdx/∫λdx = (∫2x²)/(∫2x) = (2/3)/(1) = 2/3 m — shifted towards the heavy end.
Q5 — COM of Continuous Bodies · hard · numerical
A uniform solid CONE of height 12 cm stands on its base. Its centre of mass is above the base at:
A. 6 cm
B. 8 cm
C. 4 cm
D. 3 cm ✓ Correct
Solution: COM of a solid cone is h/4 above the base = 3 cm (or 3h/4 below the apex).
Q6 — COM of Continuous Bodies · medium · numerical
A uniform semicircular disc has radius 21 cm (π ≈ 22/7). Its COM lies above the centre at 4R/3π =
A. ≈ 13.4 cm
B. ≈ 10.5 cm
C. ≈ 6.7 cm
D. ≈ 8.9 cm ✓ Correct
Solution: 4R/3π = 4×21/(3×22/7) = 84×7/66 ≈ 8.9 cm.
Q7 — COM of Continuous Bodies · hard · numerical
A rod of length L has density λ = λ₀(1 + x/L). Its COM from x = 0 is at:
A. 4L/9
B. L/2
C. 2L/3
D. 5L/9 ✓ Correct
Solution: M = λ₀(L + L/2) = 3λ₀L/2; ∫xλdx = λ₀(L²/2 + L²/3) = 5λ₀L²/6. x_cm = (5L²/6)/(3L/2) = 5L/9.
Q8 — COM of Continuous Bodies · medium · numerical
A uniform wire of length 2L is bent at its midpoint into a right angle (an L shape). The distance of the centre of mass from the corner is:
A. L√2/4 ✓ Correct
B. L√2/2
C. L/2
D. L/4
Solution: Each arm's COM is at L/2 along its axis; the combined COM is at (L/4, L/4) from the corner ⇒ distance √(L²/16 + L²/16) = L√2/4.